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Conformal Regge theory

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Abstract

We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave expansion in Mellin space, elucidating the analytic structure of the partial amplitudes. We apply the new formalism to the case of four point correlation functions between protected scalar operators in \( \mathcal{N}=4 \) Super Yang Mills, in cases where the Regge limit is controlled by the leading twist operators associated to the pomeron-graviton Regge trajectory. At weak coupling, we are able to predict to arbitrary high order in the ’t Hooft coupling the behaviour near J = 1 of the OPE coefficients \( {C_{{\mathcal{OO}J}}} \) between the external scalars and the spin J leading twist operators. At strong coupling, we use recent results for the anomalous dimension of the leading twist operators to improve current knowledge of the AdS graviton Regge trajectory — in particular, determining the next and next to next leading order corrections to the intercept. Finally, by taking the flat space limit and considering the Virasoro-Shapiro S-matrix element, we compute the strong coupling limit of the OPE coefficient \( {C_{{\mathcal{LL}J}}} \) between two Lagrangians and the leading twist operators of spin J.

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Authors and Affiliations

  1. Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal

    Miguel S. Costa, Vasco Goncalves & João Penedones

  2. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2J 2W9, Canada

    Miguel S. Costa, Vasco Goncalves & João Penedones

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  1. Miguel S. Costa
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  2. Vasco Goncalves
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  3. João Penedones
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Correspondence to Vasco Goncalves.

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ArXiv ePrint: 1209.4355

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Costa, M.S., Goncalves, V. & Penedones, J. Conformal Regge theory. J. High Energ. Phys. 2012, 91 (2012). https://doi.org/10.1007/JHEP12(2012)091

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